An afterthought squeezed into gift bag (8)
I believe the answer is:
knapsack
'bag' is the definition.
(knapsack is a kind of bag)
'an afterthought squeezed into gift' is the wordplay.
'an' becomes 'a'.
'afterthought' becomes 'ps' (ps stands for postscript).
'squeezed into' is an insertion indicator.
'gift' becomes 'knack' (knack is a kind of gift).
'a'+'ps'='aps'
'aps' placed inside 'knack' is 'KNAPSACK'.
(Other definitions for knapsack that I've seen before include "Hiker's bag" , "Bag with straps" , "Traveller's or soldier's bag" , "Hiking bag" , "Pack sank (anag.)" .)